Question

If the measure of the sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as ∠ ABC = ${75}^{\circ }$, ∠ BCD = ${35}^{\circ }$ and ∠ CDA = ${135}^{\circ }$, can you construct a quadrilateral ABCD?

• A. Yes
• B. No
• C. With the measure of $\angle$ DAB, Yes
• D. With the measure of BC, Yes

Answer 1

The correct option is D

With the measure of BC, Yes

• We cannot draw a unique quadrilateral with all the given measurements. This is because we need the measurement of two adjacent sides and 3 angles to construct the quadrilateral ABCD.
• But we are given opposite sides AB and CD. So, with the measure of BC, we will have two known adjacent sides. Hence, we will be able to construct the quadrilateral ABCD.